Series of (2+1)-dimensional stable self-dual interacting conformal field theories

Using the duality between seemingly different (2+1)-dimensional $[(2+1)d]$ conformal field theories (CFT) proposed recently [D. T. Son, Phys. Rev. X 5, 031027 (2015); M. A. Metlitski and A. Vishwanath, Phys. Rev. B 93, 245151 (2016); C. Wang and T. Senthil, Phys. Rev. X 6, 011034 (2015); C. Wang and T. Senthil, Phys. Rev. X 5, 041031 (2015); C. Wang and T. Senthil, Phys. Rev. B 93, 085110 (2016); C. Xu and Y.-Z. You, Phys. Rev. B 92, 220416 (2015); D. F. Mross et al., Phys. Rev. Lett. 117, 016802 (2016); A. Karch and D. Tong, arXiv:1606.01893; N. Seiberg et al., arXiv:1606.01989; P.-S. Hsin and N. Seiberg, arXiv:1607.07457], we study a series of $(2+1)d$ stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the $3d$ bosonic topological insulator protected by U(1) and time-reversal symmetry (T), and they remain stable as long as these symmetries are preserved. When realized as a boundary system, these CFTs can be driven into anomalous fractional quantum Hall states once T is broken. We demonstrate that the newly proposed dualities allow us to study these CFTs quantitatively through a controlled calculation, without relying on a large flavor number of matter fields. We also propose a numerical test for our results, which would provide strong evidence for the originally proposed duality between Dirac fermion and QED.